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 Sujet: proof by induction
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 Prove by induction 2009-10-02 Anonymous pose la question :How can you prove the following by induction: Any fraction (A / B), where 0 < (A / B) < 1, can be expressed as a finite sum (1 / c(1)) + (1 / c(2)) + (1 / c(3)) + ... + (1 / c(k)), where c(1), c(2), ..., c(k) are natural numbers greater than 0. [ex. (20 / 99) = (1 / 9) + (1 / 11)]Claude Tardif lui répond. Mathematical induction 2008-09-05 James pose la question :I need to prove a problem by induction regarding the Triangle Inequality. The problem is abs(a1 + a2 +...+an) <= abs(a1) + abs(a2) +...+ abs(an).Victoria West lui répond. cos(n)pi = (-1)^n 2006-12-14 Idrees pose la question :How can I prove the following: cos(n)pi = (-1)^nSteve La Rocque lui répond. A proof by induction 2006-10-02 Zamira pose la question :i'm studying induction but i don't get how to proof that 1+2+2^2+2^3+...+2^(n-1) = (2^n) - 1.Penny Nom lui répond. Proof by induction 2006-04-24 Meshaal pose la question :Find an expression for: 1-3+5 - 7 + 9 - 11 + ... + (-1)^(n-1) * (2n-1) and prove that it is correct. Stephen La Rocque lui répond. Proving a summation formula by induction 2006-04-19 Sharon pose la question :Prove by induction that the sum of all values 2^i from i=1 to n equals 2^(n+1) - 2 for n > 1.Stephen La Rocque lui répond. A proof by induction 2006-04-09 Sharon pose la question :prove by induction: For every n>1, show that 2 + 7 + 12 + ...+ (5n-3) = n(5n-1)/2Penny Nom lui répond. Proof by induction? 2005-08-10 Peter pose la question :I am a lecturer and am having a problem with the following Proof by Induction. If (N x N x N x N) + (4 x N x N x N) + (3 x N x N) + (N) = -4000 Prove that N is even! Chris Fisher and Penny Nom lui répond. Proof by induction 2004-11-20 Vic pose la question :Problem: Find the first 4 terms and the nth term of the infinite sequence defined recursively as follows: a(1) = 3 and a(k+1) = 2a(k) for k -> 1. Note: Quantities in brackets are subscripts -> means 'equal to or greater than'. Using the recursive formula, the first 4 terms are; a(1) = 3, a(2) = 6, a(3) = 12, a(4) = 24 The nth term a(n) = 2n-1 x 3 (equation 1) Equation 1 must be proven using mathematical induction. This is where I am having a problem.Penny Nom lui répond. n! > n^2 2004-03-30 Jose pose la question :How can you prove by mathematical induction that: n! > n2.Penny Nom lui répond. Proof by induction 2004-03-02 Chris pose la question :I need some help of how to solve the problem "use the principle of mathematical induction to prove that the following are true for all positive integers" cos(n x pi + X) = (-1)^n cosX any help would be appreciatedPenny Nom lui répond. Proof by induction 2002-09-26 Pooh pose la question :Use induction to show that 1 2 + 2 2 + .....+n 2 = (n 3)/3 + (n 2)/2 + n/6Paul Betts lui répond. Proof by induction 2002-08-31 Tabius pose la question :Use mathematical induction to prove that the following formulae are true for all positive integers: a) 1 + 3 + 5+...+(2n - 1) = n 2 b) 2 n > n. Penny Nom lui répond. Proof by induction 2002-02-20 Tamaswati pose la question :How do I prove the assertion that "the determinant of an upper triangular matrix is the product of the diagonal entries" by mathematical induction? (Before I check this assertion for a few values of n how do I rephrase the assertion slightly so that n appears explicitly in the assertion?)Penny Nom lui répond. Proof by induction 2001-10-16 John pose la question :Can you help me with any of these? For any natural number n > 1, prove that (4n) / (n + 1) < [(2n)!] / [(n!)2]. For any natural number n > 1, prove that 1/sqrt(1) + 1/sqrt(2) + 1/sqrt(3) + ... + 1/sqrt(n) > sqrt(n). For any natural number n and any x > 0, prove that xn + xn - 2 + xn - 4 + ... + x-n >= n + 1. Penny Nom lui répond. Proof by induction 2001-09-30 Kyle pose la question :I'm trying to learn induction and I need to see how this done please help with this problem... 20 + 21 + 22 +... + 2n = 2n+1 -1 is true whenever n is a positive integer. Penny Nom lui répond. Harmonic numbers 2001-05-23 Leslie pose la question :The harmonic numbers Hk, k = 1,2,3.....are defined by Hk = 1 + 1/2 + 1/3....1/k I am trying to prove by mathematical induction: H2n >= 1 + n/2 , whenever n is a nonnegative integer. H8 = H23 >= 1 + 3/2 Can you help? Harley Weston lui répond. Induction 2000-09-07 Joe Peterson pose la question :How do I prove by the principal of mathematical induction? 1.n+2.(n-1)+3.(n-2)+.....+(n-2).3+(n-1).2+n.1=(n(n+1)(n+2))/6 Paul Betts lui répond. Induction 2000-03-16 William Tsang pose la question :I am trying to prove a induction question Sigam r=1 n (2r -1)cube = n square (2 n square - 1) Harley Weston lui répond.

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